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    "# Adaptively Sampled Distance Fields in Julia\n",
    "\n",
    "This demonstrates basic usage of the AdaptiveDistanceFields package. This package implements the adaptive sampling described in: Sarah F. Frisken, Ronald N. Perry, and Thouis R. Jones. \"Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics\". SIGGRAPH 2000. "
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       "Plots.GRBackend()"
      ]
     },
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    }
   ],
   "source": [
    "using AdaptiveDistanceFields\n",
    "using RegionTrees: allleaves, vertices\n",
    "using StaticArrays: SVector\n",
    "using Plots\n",
    "gr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define a simple curve consisting of a line and an arc:"
   ]
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    "plt = plot([0.35, 0.35], [0.2, 0.8], color=:black, \n",
    "    aspect_ratio=:equal, legend=nothing, xlim=(0, 1), ylim=(0, 1))\n",
    "theta = linspace(-pi/2, pi/2)\n",
    "plot!(plt, 0.3 * cos.(theta) .+ 0.35, 0.3 * sin.(theta) .+ 0.5, color=:black)"
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    "We can write down the distance from any point to that curve as a fairly simple function:"
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    "function curve_distance(x)\n",
    "    if x[2] < 0.2\n",
    "        distance_to_line = norm(x - SVector(0.35, 0.2))\n",
    "    elseif x[2] > 0.8\n",
    "        distance_to_line = norm(x - SVector(0.35, 0.8))\n",
    "    else\n",
    "        distance_to_line = norm(x[1] - 0.35)\n",
    "    end\n",
    "    if x[1] >= 0.3\n",
    "        distance_to_arc = norm(norm(x - SVector(0.35, 0.5)) - 0.3)\n",
    "        return min(distance_to_arc, distance_to_line)\n",
    "    else\n",
    "        return distance_to_line\n",
    "    end\n",
    "end\n",
    "        "
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   "cell_type": "markdown",
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   "source": [
    "Let's visualize that signed distance function:"
   ]
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       "3JUN72zZsmXLN5L/B7o5P+P5uc9SAAAAAElFTkSuQmCC\n",
       "\" transform=\"translate(122, 3)\"/>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = linspace(0, 1, 101)\n",
    "y = linspace(0, 1, 101)\n",
    "plt = contour(x, y, (x, y) -> curve_distance(SVector(x, y)), \n",
    "    fill=true, legend=nothing, aspect_ratio=:equal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can approximate that function with an adaptive sampling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::AdaptiveDistanceField) (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adf = AdaptiveDistanceField(curve_distance, SVector(0., 0), SVector(1., 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can visualize the result. The adaptive sampling results in a finer grid near areas of sharp curvature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = linspace(0, 1)\n",
    "y = linspace(0, 1)\n",
    "\n",
    "# Plot the distance field\n",
    "plt = contour(x, y, (x, y) -> adf(SVector(x, y)), fill=true, \n",
    "    legend=nothing, aspect_ratio=:equal)\n",
    "\n",
    "# Draw each cell in the approximation\n",
    "for leaf in allleaves(adf.root)\n",
    "    v = hcat(collect(vertices(leaf.boundary))...)\n",
    "    plot!(plt, v[1,[1,2,4,3,1]], v[2,[1,2,4,3,1]], color=:white)\n",
    "end\n",
    "plt"
   ]
  }
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